qspec.doppler_d1  (  f ,  v ,  alpha ,  return_frame = 'atom'  )[source]

The first derivative $\frac{\partial f^\prime}{\partial v} = a\frac{f^\prime}{c}\gamma^3(v)(\frac{v}{c} - \cos(\alpha))$ with $a = \begin{cases}f / f^\prime, & \mathrm{atom}\\ -f^\prime / f, & \mathrm{lab}\end{cases}$

Parameters:

farray_like

The frequency $f$ of light (arb. units).

varray_like

The velocity $v$ of a body (m/s).

alphaarray_like

The angle $\alpha$ between the velocity- and the light-vector in the laboratory frame (rad).

return_framestr

The coordinate system for which the frequency is returned. Can be either 'atom' or 'lab'.

Returns:

outndarray

the first derivative $\partial f^\prime / \partial v$ of the Doppler-shifted frequency $f^\prime$ with respect to v in either the rest frame of the atom or the laboratory frame ([f] s/m).

Raises:

ValueError

return_frame must be either 'atom' or 'lab'.